The Shape of Free Surface in Squeeze and Fountain Flows Evan Mitsoulis and Andreas Matsoukas School of Mining Engineering & Metallurgy, National Technical University of Athens, Zografou, 157 80 Athens, Greece Abstract Two related problems in polymer processing deal with the free surface present in squeeze flow of plastometers and the fountain flow in injection molding. Although these problems have been solved in the past by various researchers, a more careful examination can reveal similarities and differences that play a role for different materials. The present work reviews these previous efforts. In addition it offers new results from full parametric studies of the geometric parameter (aspect ratio) in squeeze flow, and of the material parameters for both flows for different fluids. Newtonian, pseudoplastic and viscoplastic models are considered. Both axisymmetric and planar geometries are studied. The emphasis is on determining the extent and shape of the free surface, and in the case of viscoplastic materials, the location of yielded / unyielded regions for a wide range of Bingham numbers. The free surface shapes are similar but not identical in the two problems, as are the unyielded regions. The present results extend previous simulations and are offered as benchmark solutions for these important polymer-processing problems. 1 Introduction In polymer processing, two important processes are compression molding and injection molding [1]. The principles of compression molding are also to be found in plastometry and lead to the related problem of squeeze flow [2]. In this case, a material is squeezed between two circular disks (Fig. 1a) or parallel plates, and the material moves radially outwards from the center. In the case of injection molding, the material flows in the mold under pressure, advancing forward and acquiring a free surface at the front (Fig. 1b). This type of flow is termed fountain flow [1] and has been the object of many investigations in the past, both experimentally and computationally [3]. r z θ ΔRCL 2H R V A B C D (a) (b) Figure 1: (a) Squeeze flow in a plastometer; (b) Fountain flow in injection molding. What is common in both problems is the development of a free surface at the moving front. Both problems have been solved in the past [3-5], but no attention was paid to the details of each case with regard to the free surface development for various different materials. It is the purpose of the present work to study in detail these two model flows and offer new results for pseudoplastic (power-law) and viscoplastic (Bingham) fluids that represent a wide variety of materials used in polymer processing. 2 Mathematical Modelling 2.1 Squeeze flow The problem of the squeeze flow with free surface between two coaxial disks of radius R and gap 2H is schematically depicted in Fig. 1(a) and originally refers to an axisymmetric geometry [2]. In the corresponding planar geometry L defines half the length of the plates in the y-